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Seismic pounding between adjacent buildings is an undesirable phenomenon. Depending on the characteristics of the colliding buildings, pounding might cause severe structural damage in some cases, and even collapse is possible in some extreme situations. In order to mitigate the risk of seismic pounding between new buildings, current seismic design codes prescribe a minimum separation distance between adjacent structures. The value of the minimum separation distance is assumed equal to the peak relative displacement computed at the most likely pounding location and corresponding to a site-specific seismic intensity. Examining the collision possibility of adjacent structures as a result of earthquake is the basis of formulating regulations for determining minimum dimensions of separation distances. This distance can be calculated in different ways. In previous studies, double difference combination has been generally used to determine this distance and their only difference is in determining correlation coefficient of seismic response in two adjacent systems. This coefficient which depends on period and damping of the two systems has been obtained in previous works with the assumption of a linear behavior of structures. In the nonlinear range, the same correlation coefficient obtained from the linear mode is used by making structure behavior equivalent to linear mode and introducing values of effective damping and period. Modified values of period and damping depend on the requirement of system ductility under the applied record, which has been obtained for a specific behavioral model and from numerous numerical studies. In this study, the correlation coefficient of the two systems was presented using random vibration equations for the systems by Bouc - Wen different hysteresis behavior model. Moreover, the proposed relation could be applied for different input stimulation with specific spectral density and is more comprehensive than previous relations. Ductility demand of the system corresponding to the input spectral density was determined by random vibration relations and the probability distribution of relative displacement between the two systems which was obtained from the presented relations was compared with the existing ones. This study evaluates the accuracy of two different criteria to calculate the separation necessary to prevent seismic pounding between nonlinear hysteretic structural systems. All of the criteria considered in this paper make use of the same basic equation of the Double Difference Combination rule, but they adopt different procedures to estimate the correlation between displacement responses of nonlinear hysteretic systems. Monte Carlo analysis used to verify the relations presented for two adjacent nonlinear systems under the applied record which were simulated by a specified spectral density in stationary and non-stationary forms. Results obtained through Monte Carlo simulations indicate that the relation presented in this study is completely satisfactory and none of the two criteria evaluated in this study is exact.

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This paper briefly reviews Fiber Reinforced Elastomeric Isolators (FREIs) as a relatively new type of elastomeric bearings. In comparison with conventional Steel Reinforced Elastomeric Isolators (SREIs) that are reinforced with steel plates, FREIs utilize fiber fabric layers as the reinforcement material. The fiber reinforcement is employed to prevent the lateral bulging of elastomer layers when the bearing is subjected to vertical compression. Fiber reinforced isolators are categorized in two groups, namely, “bonded-“ and “unbonded-“ FREIs, depending on the boundary conditions at top and bottom surfaces of the bearing. The main objective of this paper is to simulate the lateral load-displacement hysteresis loops of unbonded-FREIs. In an unbonded-FREI, no bonding is provided between the bearing and its top and bottom contact supports. As such, shear forces are transferred via friction at the contact surfaces. When an unbonded-FREI is deformed laterally, portion of its contact surfaces roll off the contact supports, and the bearing exhibits a specific deformation called “rollover deformation”. As a result of rollover deformation, the effective lateral stiffness of the bearing is decreased significantly. This in turn improves the seismic isolation efficiency due to the increased base isolated period of bearing. The ultimate lateral displacement in an unbonded-FREI may achieve when the originally vertical faces of the bearing contact top and bottom supports. Lateral load-displacement response in an unbonded-FREI is characterized with a gradual softening (due to rollover deformation) that is followed by a stiffening behavior at the ultimate stage of lateral bearing displacement. Under a cyclic excitation, the response characteristics of the bearing during the first load-cycle are different than the subsequent cycles of the same load amplitude. This phenomenon that is specific to elastomeric materials is known as Mullins’ effect. In this paper an extended Bouc-Wen model is developed to simulate the lateral load-displacement hysteresis loops of unbonded-FREIs. The model captures the gradual softening and ultimate stiffening behavior in the load-displacement curve of the bearing, and addresses the Mullins’ effect in the simulation of hysteresis loops. The proposed model comprises two simultaneous coupled equations which employ six constant coefficients altogether. To determine these coefficients, the model is fitted to experimentally-evaluated load-displacement hysteresis loops of prototype bearings. The experimental loops are obtained from cyclic shear tests that are conducted on the bearing while it is subjected to constant vertical compression. In order to account for Mullins’ effect, an individual set of coefficients corresponding to unscragged loops (the first cycle of each displacement amplitude) are evaluated. The second set of coefficients is attributed to scragged response (subsequent cycles of each displacement amplitude) of the bearing. To simulate the load-displacement hysteresis loops, the proposed model switches between the first and the second set of coefficients depending on the unscragged or scragged state of the elastomer, respectively. A constraint is imposed on the model to assure its continuity when the model coefficients are alternated. Comparison between analytical and experimental results (shake-table test data) indicates that the proposed model is accurate in dynamic response simulation of the unbonded-FREIs studied in this paper.

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Abstract: In recent years nonlinear static analysis method has been widely used in the field of performance based earthquake engineering. Whereas the capabilities of this method is well recognized, it still has inherent shortcomings. Accordingly, by considering aspects such as nonlinear properties of members, higher modes effect, and the computational cost, the accuracy of the method should be investigated. Although an enormous study have been carried out to improve the pushover analysis, the proposed methods are almost deterministic and cannot directly consider the seismic records uncertainties. Toward this challenge, the present study aims to examine the requirements of inelastic static analysis method through a comparison with incremental dynamic analysis results. The general purpose of the pushover method is to yield the maximum story responses (shear and drift) expected during the earthquake. For this reason, the selection of the dynamic response absolute maxima is discussed and different criteria are investigated; maximum displacement versus corresponding base shear, maximum displacement versus maximum base shear and, finally, maximum base shear versus corresponding displacement. Therefore, using the information obtained from dynamic analysis, the characteristic of the proper lateral forces that can represent the average of the maximum effect of the ensemble of earthquake records and consider the inherent records uncertainties, can be obtained. So, to derive the characteristics of equivalent lateral forces based on the dynamic response of the system, four different lateral force profiles can be considered; (1) F1: lateral forces create the same average story forces as dynamic analysis, (2) F2: the profile and intensity of the lateral forces that produce the average of the maximum story shear induced by seismic record ensemble, (3) D1: the lateral force profile is chosen in a way that it can produce the same maximum story drifts as dynamic analysis, and (4) D2: the forces that their responses best represent the average of the story lateral displacement in dynamic analysis. The comparisons are performed for three levels of the typical small, medium and high-rise buildings denoted as four, twelve and twenty-story shear frames. The mathematical model of the frames are chosen as the smoothly varying differential Bouc–Wen model. Because of the versatility and mathematical tractability of the Bouc-Wen model, by altering different parameters of the model, it can simulate various structural behavior with any degree of nonlinearity. The estimated responses are compared to those resulted from the nonlinear dynamic analysis. The comparison procedure in the validation process is conducted in two levels; structural global level results (base shear and roof displacement) and story level results (the story drift and lateral force profiles). Furthermore, using the considered characteristics of the lateral load profile, the probabilistic capacity curve which has the potential to be used for assessing different parts of the structure for different performance levels is extracted. As we expect from static nonlinear analysis the demand of the stories should reach their maximum. In fact, in the low-rise structure when the roof displacement reach its maximum, all of the stories also lean towards their maximum demands. By increasing the structures height (followed with higher modes effect), the result of classic pushover analysis cannot correctly estimate the demands and it differs from the result of dynamic analysis.